She veered to the left, mounted a footpath, and hit a power pole.
The children were unhurt.
Reilly initially attempted to drive off, but was stopped by a member of the public who reached in, removed the car keys and called police.
When spoken to by police, she claimed her driving had been affected by 'three valium' she had taken earlier in the day.
Today, her lawyer Mr Fletcher rejected claims that one of the children was unrestrained, saying the child was in a booster seat that was inappropriate for their age.
He said there was "limited damage" to the car, with just a crack to the bumper, but Reilly accepted her blood alcohol level was "astronomical".
The beneficiary got behind the wheel because a child had not come home, but accepted her reasoning had "left her" by then.
Mr Fletcher asked the judge to step back from home detention because she had to care for her family.
Reilly, who earlier admitted charges of careless driving and driving with excess breath alcohol, now had care of four children, Mr Fletcher said.
Her house was also in the earthquake-hit residential red zone, and she will need to move out by the end of April.
Judge Phillip Moran accepted that Reilly suffered addictions that had "bedevilled" her life, was on medication for anxiety, and was not a "hardened criminal".
But he was concerned it was her sixth conviction for drink driving - the previous was four years ago - and that she had an accident with children in the car who were "exposed to risk".
Community service was not appropriate, and he sentenced her to six months' home detention at her New Brighton home, with special conditions that she must attend drug and alcohol rehabilitation programmes.
She was also disqualified from driving indefinitely, and can not reapply for a new licence within 12 months.
